Question

Calculati sin 75°*cos 15°

Answer 1

sin75*cos15

=sin(45+30)*cos(45-30)
=(sin45*cos30+cos45*sin30)*(cos45*cos30+sin45*sin30)
=(√2*√3/4+√2*1/4)*(√2*√3/4+√2*1/4)
=(√6/4+√2/4)²
=(6+2+4√3)/16
=(2+√3)/4

Answer 2

sin 75° = cos (90°-75°)= cos 15°
sin75° * cos 15° = cos^2 15° 
cos^2(2a)= cos^2(a) - sin^2(a) = 2cos^2(a) -1, unde a = 15°, in cazul nostru ⇒ cos^2(15°) = [1+cos^2(30°)] : 2 =
(1 + rad3 / 2):2= (2+rad3) :4
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